epi_π_app_zero_of_epi — Mathlib

English

An equivalence of IsLimit between forks associated to P.map π.op and the user-defined equalizer construction.

Русский

Эквивалентность IsLimit между форками, связанными с P.map π.op и указанной конструкцией равнозначителя.

LaTeX

$$isLimit_forkOfι_equiv (P) (π) (c) (hc)$$

Lean4

theorem epi_π_app_zero_of_epi [HasSheafify (coherentTopology C) (Type v)]
    [Balanced (Sheaf (coherentTopology C) (Type v))] [(coherentTopology C).WEqualsLocallyBijective (Type v)]
    {F : ℕᵒᵖ ⥤ Sheaf (coherentTopology C) (Type v)} {c : Cone F} (hc : IsLimit c)
    (hF : ∀ n, Epi (F.map (homOfLE (Nat.le_succ n)).op)) : Epi (c.π.app ⟨0⟩) :=
  by
  simp_rw [← Sheaf.isLocallySurjective_iff_epi'] at hF ⊢
  exact isLocallySurjective_π_app_zero_of_isLocallySurjective_map hc hF h

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